London in the 1960s was as central to the look and feel of that fabled era as any place on earth. The music that emerged from England (the Beatles, the Stones, the Who, Cream and countless others) was, in large part, the soundtrack of the Sixties. The street scenes, especially along Carnaby Street in Soho, with Mods and hippies parading their utterly distinctive gear, provided youth culture around the world with exemplars of cool that are still embraced today.

Finally, the fashions that emerged from London, as well as the models who made those fashions both hip and famous, still echo through pop culture. Jean Shrimpton, Penelope Tree and, of course, the extraordinary woman known as Twiggy (born Lesley Hornby) were, for several years in the mid-1960s, the heavily made-up faces of Swinging London itself.

Today, Twiggy remains not only a fashion touchstone—with any slim young thing who sports short hair and liberal eye shadow inevitably pegged as “Twiggy-like”—but has also, incredibly, managed to stay relevant and productive for decades. Rather than simply and endlessly recycling the elements of her appeal that made her famous in the first place, Hornby went on to act in films and on stage (not just in set pieces, but in classic plays by heavyweights like Shaw and Noel Coward); recorded—and continues to record—as a singer; appeared on TV shows (like all great stars, for example, she took a turn on The Muppets); and wrote several books, including a well-received autobiography.

It sometimes astonishes people—or people outside the UK, at least—to learn that the skinny, blonde, mop-topped, teenaged model who took the fashion world by storm in the Sixties actually survived those crazy years, grew up and, incredibly, is still around.

Here, on Twiggy’s 65rd birthday, LIFE.com celebrates her career and her enduring style with a series of rare pictures—shot in California for a feature that never appeared in the magazine—by long-time LIFE photographer Ralph Crane. Captured at the very height of her fame as one of the first-ever supermodels, and during her first visit to the U.S. when she was all of 18 years old, the Twiggy in most of these pictures seems remarkably cool and sophisticated for one so young. (Perhaps not surprising, considering that she’d been one of the most famous figures—and had one of the most famous figures—in the world for the previous whirlwind year.)

In other shots, meanwhile, she looks refreshingly like a teen who is still thrilled that her life has taken her to these sorts of places, with these sorts of people. There are other Sixties icons here, after all—Sonny and Cher, for example, and Steve McQueen (wearing a shearling coat in the Beverly Hills sun, and somehow looking cool doing it).

Throughout it all, the vibe of all of these photos is distinctly, unmistakably that of the Sixties—specifically, that brief period in 1966 and 1967, before MLK and Bobby Kennedy were assassinated, before Altamont, before the Manson family murders, before the decade died out entirely, when people might have been able to convince themselves that the Age of Aquarius was really just around the corner. Or, if not the Age of Aquarius, then at least a pretty groovy garden party at a mansion in Beverly Hills.